def approxUpdateEig(self, subW, ABBA, omega, Q):
        """
        Update the eigenvalue decomposition of ABBA
        """
        # --- remove rows/columns ---
        if self.n > ABBA.shape[0]:
            omega, Q = EigenUpdater.eigenRemove(omega, Q, ABBA.shape[0],
                                                min(self.k2, ABBA.shape[0]))

        # --- update existing nodes ---
        currentN = min(self.n, ABBA.shape[0])
        deltaDegrees = numpy.array(
            subW.sum(0)).ravel()[0:currentN] - self.degrees[:currentN]
        inds = numpy.arange(currentN)[deltaDegrees != 0]
        if len(inds) > 0:
            Y1 = ABBA[:currentN, inds] - self.ABBALast[:currentN, inds]
            Y1 = numpy.array(Y1.todense())
            Y1[inds, :] = Y1[inds, :] / 2
            Y2 = numpy.zeros((currentN, inds.shape[0]))
            Y2[(inds, numpy.arange(inds.shape[0]))] = 1
            omega, Q = EigenUpdater.eigenAdd2(omega, Q, Y1, Y2,
                                              min(self.k2, currentN))

        # --- add rows/columns ---
        if self.n < ABBA.shape[0]:
            AB = numpy.array(ABBA[0:self.n, self.n:].todense())
            BB = numpy.array(ABBA[self.n:, self.n:].todense())
            omega, Q = EigenUpdater.lazyEigenConcatAsUpdate(
                omega, Q, AB, BB, min(self.k2, ABBA.shape[0]))

        return omega, Q
    def approxUpdateEig(self, subW, ABBA, omega, Q):
        """
        Update the eigenvalue decomposition of ABBA
        """
        # --- remove rows/columns ---
        if self.n > ABBA.shape[0]:
            omega, Q = EigenUpdater.eigenRemove(omega, Q, ABBA.shape[0], min(self.k2, ABBA.shape[0]))

        # --- update existing nodes ---
        currentN = min(self.n, ABBA.shape[0])
        deltaDegrees = numpy.array(subW.sum(0)).ravel()[0:currentN]- self.degrees[:currentN]
        inds = numpy.arange(currentN)[deltaDegrees!=0]
        if len(inds) > 0:
            Y1 = ABBA[:currentN, inds] - self.ABBALast[:currentN, inds]
            Y1 = numpy.array(Y1.todense())
            Y1[inds, :] = Y1[inds, :]/2
            Y2 = numpy.zeros((currentN, inds.shape[0]))
            Y2[(inds, numpy.arange(inds.shape[0]))] = 1
            omega, Q = EigenUpdater.eigenAdd2(omega, Q, Y1, Y2, min(self.k2, currentN))

        # --- add rows/columns ---
        if self.n < ABBA.shape[0]:
            AB = numpy.array(ABBA[0:self.n, self.n:].todense())
            BB = numpy.array(ABBA[self.n:, self.n:].todense())
            omega, Q = EigenUpdater.lazyEigenConcatAsUpdate(omega, Q, AB, BB, min(self.k2, ABBA.shape[0]))
        
        return omega, Q
    def testEigenConcat(self):
        tol = 10**-6

        for i in range(3):
            m = numpy.random.randint(10, 20)
            n = numpy.random.randint(5, 10)
            p = numpy.random.randint(5, 10)
            #            A = numpy.zeros((m, n), numpy.complex)
            #            B = numpy.zeros((m, p), numpy.complex)
            #            A.real = numpy.random.randn(m, n)
            #            A.imag = numpy.random.randn(m, n)
            #            B.real = numpy.random.randn(m, p)
            #            B.imag = numpy.random.randn(m, p)
            A = numpy.random.randn(m, n)
            B = numpy.random.randn(m, p)

            #logging.debug("m="+str(m)+" n="+str(n)+" p="+str(p))

            AcB = numpy.c_[A, B]
            ABBA = AcB.conj().T.dot(AcB)

            AA = ABBA[0:n, 0:n]
            AB = ABBA[0:n, n:]
            BB = ABBA[n:, n:]

            lastError = 1000
            lastError2 = 1000

            for k in range(1, n):
                #logging.debug("k="+str(k))
                #First compute eigen update estimate
                omega, Q = numpy.linalg.eig(AA)
                pi, V = EigenUpdater.eigenConcat(omega, Q, AB, BB, k)
                ABBAEst = V.dot(numpy.diag(pi)).dot(V.conj().T)

                t = min(k, Util.rank(ABBA))
                self.assertTrue(pi.shape[0] == t)
                self.assertTrue(
                    numpy.linalg.norm(V.conj().T.dot(V) - numpy.eye(t)) < tol)

                #Second compute another eigen update estimate
                omega, Q = numpy.linalg.eig(AA)
                pi2, V2, D2, D2UD2 = EigenUpdater.lazyEigenConcatAsUpdate(
                    omega, Q, AB, BB, k, debug=True)
                ABBAEst2 = V2.dot(numpy.diag(pi2)).dot(V2.conj().T)

                U = ABBA.copy()
                U[0:n, 0:n] = 0
                self.assertTrue(
                    numpy.linalg.norm(U -
                                      D2.dot(D2UD2).dot(D2.conj().T)) < tol)

                t = min(k, Util.rank(ABBA))
                self.assertTrue(
                    numpy.linalg.norm(V2.conj().T.dot(V2) -
                                      numpy.eye(pi2.shape[0])) < tol)

                #Compute estimate using eigendecomposition of full matrix
                sfull, Vfull = numpy.linalg.eig(ABBA)
                indsfull = numpy.flipud(numpy.argsort(numpy.abs(sfull)))
                Vfull = Vfull[:, indsfull[0:k]]
                sfull = sfull[indsfull[0:k]]
                ABBAEstfull = Vfull.dot(numpy.diag(sfull)).dot(Vfull.conj().T)

                #The errors should reduce
                error = numpy.linalg.norm(ABBAEst - ABBA)
                if Util.rank(ABBA) == k:
                    self.assertTrue(error <= tol)
                lastError = error

                error = numpy.linalg.norm(ABBAEst2 - ABBA)
                self.assertTrue(error <= lastError2 + tol)
                lastError2 = error
    def testEigenConcat(self):
        tol = 10**-6
        
        for i in range(3): 
            m = numpy.random.randint(10, 20)
            n = numpy.random.randint(5, 10)
            p = numpy.random.randint(5, 10)
#            A = numpy.zeros((m, n), numpy.complex)
#            B = numpy.zeros((m, p), numpy.complex)
#            A.real = numpy.random.randn(m, n)
#            A.imag = numpy.random.randn(m, n)
#            B.real = numpy.random.randn(m, p)
#            B.imag = numpy.random.randn(m, p)
            A = numpy.random.randn(m, n)
            B = numpy.random.randn(m, p)

            #logging.debug("m="+str(m)+" n="+str(n)+" p="+str(p))

            AcB = numpy.c_[A, B]
            ABBA = AcB.conj().T.dot(AcB)

            AA = ABBA[0:n, 0:n]
            AB = ABBA[0:n, n:]
            BB = ABBA[n:, n:]

            lastError = 1000
            lastError2 = 1000

            for k in range(1,n):
                #logging.debug("k="+str(k))
                #First compute eigen update estimate
                omega, Q = numpy.linalg.eig(AA)
                pi, V = EigenUpdater.eigenConcat(omega, Q, AB, BB, k)
                ABBAEst = V.dot(numpy.diag(pi)).dot(V.conj().T)

                
                t = min(k, Util.rank(ABBA))
                self.assertTrue(pi.shape[0] == t)
                self.assertTrue(numpy.linalg.norm(V.conj().T.dot(V) - numpy.eye(t)) < tol)

                #Second compute another eigen update estimate
                omega, Q = numpy.linalg.eig(AA)
                pi2, V2, D2, D2UD2 = EigenUpdater.lazyEigenConcatAsUpdate(omega, Q, AB, BB, k, debug=True)
                ABBAEst2 = V2.dot(numpy.diag(pi2)).dot(V2.conj().T)


                U = ABBA.copy()
                U[0:n, 0:n] = 0
                self.assertTrue(numpy.linalg.norm(U - D2.dot(D2UD2).dot(D2.conj().T)) < tol )

                t = min(k, Util.rank(ABBA))
                self.assertTrue(numpy.linalg.norm(V2.conj().T.dot(V2) - numpy.eye(pi2.shape[0])) < tol)

                #Compute estimate using eigendecomposition of full matrix
                sfull, Vfull = numpy.linalg.eig(ABBA)
                indsfull = numpy.flipud(numpy.argsort(numpy.abs(sfull)))
                Vfull = Vfull[:, indsfull[0:k]]
                sfull = sfull[indsfull[0:k]]
                ABBAEstfull = Vfull.dot(numpy.diag(sfull)).dot(Vfull.conj().T)

                #The errors should reduce
                error = numpy.linalg.norm(ABBAEst - ABBA)
                if Util.rank(ABBA)==k:
                    self.assertTrue(error <= tol)
                lastError = error

                error = numpy.linalg.norm(ABBAEst2 - ABBA)
                self.assertTrue(error <= lastError2+tol)
                lastError2 = error